Related papers: The Lasserre hierarchy for equiangular lines with …
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy…
We obtain several new results contributing to the theory of real equiangular line systems. Among other things, we present a new general lower bound on the maximum number of equiangular lines in d dimensional Euclidean space; we describe the…
We give upper-bounds for the dimension of some linear systems. The theorem improves the differential Horace method introduced by Alexander-Hirschowitz, and was conjectured by Simpson. Possible applications are the calculus of the dimension…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
In this paper we generalize in Lorentz-Minkowski space $\l^3$ the two-dimensional analogue of the catenary of Euclidean space. We solve the Dirichlet problem for bounded mean convex domains and spacelike boundary data that have a spacelike…
Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…
For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear…
Left-invariant Lorentzian structures on the 2D solvable non-Abelian Lie group are studied. Sectional curvature, attainable sets, Lorentzian length maximizers, distance, spheres, and infinitesimal isometries are described.
The symmetry group structures of two dimensional coupled nonlinear Shr\"{o}dinger equations are considered. We first show that the equations admit infinite dimensional symmetry algebra as well as the corresponding symmetry group depending…
Whereas Lie had linearized scalar second order ordinary differential equations (ODEs) by point transformations and later Chern had extended to the third order by using contact transformation, till recently no work had been done for higher…
We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from [arXiv:1410.8816] in two ways 1) relaxing the requirement of affineness and 2) extending to fractional optimization problems.…
By using Lie symmetry methods, we identify a class of second order nonlinear ordinary differential equations invariant under at least one dimensional subgroup of the symmetry group of the Ermakov-Pinney equation. In this context, nonlinear…
In this paper, claims by Lemmens and Seidel in 1973 about equiangular sets of lines with angle $1/5$ are proved by carefully analyzing pillar decompositions, with the aid of the uniqueness of two-graphs on $276$ vertices. The Neumann…
A sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity properties of solutions to nonlinear elliptic…
We study the convergence rate of a hierarchy of upper bounds for polynomial minimization problems, proposed by Lasserre [SIAM J. Optim. 21(3) (2011), pp. 864-885], for the special case when the feasible set is the unit (hyper)sphere. The…
This paper presents high-order numerical methods for solving boundary value problems associated with the Lane-Emden equation, which frequently arises in astrophysics and various nonlinear models. A major challenge in studying this equation…
We first review some topics in the classical computational geometry of lines, in particular the O(n^{3+\epsilon}) bounds for the combinatorial complexity of the set of lines in R^3 interacting with $n$ objects of fixed description…
The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…